Abstract

This study was conducted to look at some cognitive (working memory and field dependency) and attitudinal factors which relate to learning and teaching mathematics. The purpose was to suggest ways that might help to improve students’ performance in mathematics. A multi-step strategy was used to examine the relationship between these variables and learning mathematics. The first and the second steps focussed on the students and the third step looked at the mathematics teachers and inspectors ideas about learning and teaching mathematics.
This research has investigated the influence of working memory capacity and field dependency on mathematics achievement. The working memory space and the degree of field dependency were measured for 1346 school students aged between 14-16 years from public schools in Kuwait. The Digit Backward Test was used to determine working memory space, and the Group Embedded Figure Test was used to measure the degree of field-dependency for the students, both these tests have been used widely and their validity is assured. However, absolute measurements were not important in this study, as rank order was all that was required.
In order to investigate the correlations between performance in different topics in mathematics and the working memory space and field dependency, mathematics tests were developed where some questions had high working memory demand and others had very low working memory demand. Furthermore, in order to investigate which versions of tasks will lead to improved mathematics performance, some questions were presented as symbolic tasks; others were presented as visual tasks; some of them presented as abstract tasks and others related to life.
This study also explored the attitudes of the students towards mathematics in the following areas: the importance of mathematics as a discipline; attitudes towards learning mathematics; confidence in mathematics classes; the relationship between attitudes and achievement; activities in mathematics classes, and opinions about mathematicians.
The perceptions of mathematics teachers and inspectors were investigated to see the extent to which their views related to the findings from work with students. A sample of 25 mathematics teachers and 4 mathematics inspectors was selected randomly and they were interviewed to compare their views. This step involved semi-structured interviews which offered an opportunity to focus on some key areas as well as giving freedom for the teachers to expand their views.
The results indicated that field dependent students with low working memory capacity perform badly in mathematics. This might be attributed to their inability to distinguish between relevant and irrelevant items, with consequent working memory overload. Evidence shows that the way the questions or the problems are given to the students is very important for the students to understand and to succeed in solving them. Complicated shapes or long involved text are both more likely to produce overloading of the working memory space. Therefore, the study recommends that teachers should organise their material with great care in order that students are not penalised for some personal characteristic over which they have no control.
This study also showed a clear evidence of a decline in attitudes with age and the excessively overloaded curriculum was a likely reason along with the perceptions that some topics were irrelevant. Furthermore, this study reflects the crucial role that the mathematics teacher plays in the formation of student attitudes towards mathematics. Thus, aiming to develop positive attitudes towards mathematics including confidence, enjoyment and an appreciation of it as a powerful tool should be parallel with the acquisition and the understanding of mathematics concepts and skills in mathematics education.
Finally, the interviews show that there is no agreement about the objectives of mathematics education in Kuwait between those who decide the syllabuses (mathematics inspectors) and those who are going to teach these syllabuses (mathematics teachers). When the issue of the purpose for mathematics education is agreed, then it may be possible to consider what topics might further these aims most fully. In fact, teachers are involved daily in the teaching processes and they know the population of their students very well. Thus, their views about the syllabuses should be taken into consideration and they should be involved in the process of deciding the syllabuses.
The study has major implications for the development of mathematics education in Kuwait but many of the findings will be widely applicable in other educational systems.